A digitally recorded gray value image contains image data which are shown in different gray values. If such images are formed, for example, by means of an electron microscope, an electron beam scans line by line over the specimen area to be investigated. If this is done at high speed, then noise or a granulation arise which clearly and disturbingly are superposed on the actual image data. An image recorded in such a manner can only be detected with difficulty and with great relative uncertainty by a viewer. If an electron beam is guided over the specimen at a very slow speed, then image elements can only be imaged unsharply or blurred because mechanical and electronic disturbances become effective in an amplified manner because of a long integration time per image point. Recordings of this kind can be improved with a digital image reprocessing, for example, via a noise filter, so that the ratio of signal to noise is increased. In this way, gray values of neighboring pixels are often summed and averaged. While the noise is reduced thereby, the resolution of the image deteriorates. This relationship can, in principle, not be avoided by using a noise filter.